# An object with a mass of 4 kg is hanging from an axle with a radius of 8 cm. If the wheel attached to the axle has a radius of 24 cm, how much work would it take to turn the wheel 2 cm?

Apr 23, 2016

As shown in the figure
The radius of the Wheel $R = 24 c m$
The radius of the Axle $r = 8 c m$
The mass of the object $m = 4 k g$
The Weightof the object $W = m g = 4 \times 9.8 N$
P is the applied force.
The Displacement of Applied force(P) $= d = 2 c m = 0.02 m$
The working principle of wheel -axle system may be compared with the working principle of First Kind of lever

So
$P \times R = W \times r \implies P = W \times \frac{r}{R} = 4 \times 9.8 \times \frac{8}{24} N$

Hence the Work done $= P \times d = 4 \times 9.8 \times \frac{8}{24} \times 0.02 J = 0.26 J$